Bounce and give in your table will cause you trouble. Find a sturdy place to cut. One thing I do to keep my fabric from wondering at the end of a cut is to pre- cut the end of the cut. The first cut I make when I have the material and ruler aligned is at the end of the cut about one inch long. My fabric never wonders. Try it sometime and if you fnd it works, great.
EDIT: I posted this trick a whle ago. The pic shows a single piece of fabric but works for folded fabric as well.
http://www.quiltingboard.com/main-f1...p-t136061.html